# 01-平均差「Mean Deviation」

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• 数据分析
• 数据分析

## # 怎样计算

• 一、求所有数据值的平均值open in new window
• 二、求每个数据与平均值的距离（用数据值减去平均值，不理正负号）
• 三、求这些距离的平均

36
63
63
72
81
112
156
167

（没有正负号！）

|-3| = 3

## # 总和符号

"加起来" 的符号是 Σ（叫总和符号open in new window)，所以：

## # 例子： 3、6、6、7、8、11、15、16 的 平均差

### # 一、求平均：

$\hugeμ=\frac{3+6+6+7+8+11+15+16}{8}=\frac{72}{8}=9$

## # 平均差的意思是什么？

### # 一、求平均：

$\hugeμ=\frac{600+470+170+430+300}{5}=\frac{1970}{5}=394$

x|x - μ|
600206
47076
170224
43036
30094
Σ|x - μ| = 636

### # 三、求平均差：

（可以和 147 mm标准差open in new window比较一下）

## # 检测

### # 例子：3、6、6、7、8、11、15、16

6 + 3 + 3 + 2 + 1 = 2 + 6 + 7

15 = 15

## # Question

### # Question 1

Calculate the mean deviation for the numbers: 75, 83, 96, 100, 121 and 125

A. 14.33

B. 15

C. 15.33

D. 16

Step 1 Find the mean:

μ = (75 + 83 + 96 + 100 + 121 + 125) ÷ 6 = 600 ÷ 6 = 100

Step 2 Find the Absolute Deviations:

Step 3 Find the Mean Deviation:

### # Question 2

Ten friends scored the following marks in their end-of-year math exam: 23%, 37%, 45%, 49%, 56%, 63%, 63%, 70%, 72% and 82%

What was the mean deviation of their marks?

A. 14%

B. 15%

C. 16%

D. 17%

Step 1 Find the mean:

μ = (23 + 37 + 45 + 49 + 56 + 63 + 63 + 70 + 72 + 82) ÷ 10 = 560 ÷ 10 = 56%

Step 2 Find the Absolute Deviations:

Step 3 Find the Mean Deviation:

### # Question 3

A booklet has 12 pages with the following numbers of words: 271, 354, 296, 301, 333, 326, 285, 298, 327, 316, 287 and 314

What is the mean deviation of the number of words per page?

A. 18.5

B. 19.33

C. 20

D. 20.17

Step 1 Find the mean:

μ = (271 + 354 + 296 + 301 + 333 + 326 + 285 + 298 + 327 + 316 + 287 + 314) ÷ 12 = 3,708 ÷ 12 = 309

Step 2 Find the Absolute Deviations:

Step 3 Find the Mean Deviation:

### # Question 4

What is the mean deviation of the first 10 numbers of the Fibonacci sequence?

A. 8.8

B. 8.5

C. 8.42

D. 8.32

The first 10 numbers of the Fibonacci sequence are: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34

Step 1 Find the mean:

μ = (0 + 1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34) ÷ 10 = 88 ÷ 10 = 8.8

Step 2 Find the Absolute Deviations:

Step 3 Find the Mean Deviation:

### # Question 5

The Lakers scored the following numbers of goals in their last twenty matches: 3, 0, 1, 5, 4, 3, 2, 6, 4, 2, 3, 3, 0, 7, 1, 1, 2, 3, 4, 6

Calculate the Mean Deviation.

A. 1.5

B. 2

C. 2.5

D. 3

Method 1

Step 1 Find the mean:

μ = (3 + 0 + 1 + 5 + 4 + 3 + 2 + 6 + 4 + 2 + 3 + 3 + 0 + 7 + 1 + 1 + 2 + 3 + 4 + 6) ÷ 20 = 60 ÷ 20 = 3

Step 2 Find the Absolute Deviations:

Step 3 Find the Mean Deviation:

Method 2 This can be done much more neatly using tables, as follows:

First complete a frequency table:

Then calculate the mean and mean deviation from the following table:

### # Question 6

Ramiro did a survey of the number of pets owned by his classmates, with the following results:

What was the mean deviation of the number of pets?

A. 1.02

B. 1.053

C. 1.087

D. 1.12

Calculate the mean and mean deviation from the following table:

### # Question 7

Emma rolled a die a number of times and recorded her results in a bar graph, as follows:

What was the mean deviation of the scores?

A. 1.375

B. 1.5

C. 1.625

D. 1.875

First complete a frequency table:

Then calculate the mean and mean deviation from the following table:

### # Question 8

Rachel rolled a die forty five times with the following results:

What was the mean deviation of her scores?

A. 1.564

B. 1.609

C. 1.64

D. 1.653

Calculate the mean and mean deviation from the following table:

### # Question 9

A spinner is in the shape of a regular heptagon marked with the numbers 1 to 7.

Theodore spun the spinner 50 times and recorded his results in a table, as follows:

Calculate the mean deviation of the scores.

A. 1.6088

B. 1.7288

C. 1.7688

D. 1.8088

Calculate the mean and mean deviation from the following table:

### # Question 10

The children in a class did a survey of the number of siblings (brothers and sisters) each of them had. The results are recorded in the following table:

Calculate the mean deviation of the number of siblings.

A. 1.38

B. 1.41

C. 1.45

D. 1.48

Calculate the mean and mean deviation from the following table:

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